When it comes to the notion of minds, it's something that we are all intimately familiar with. "Cogito, ergo sum" is something we all can recognise instantly and understand the implications.
I think this, however, gives the false impression that we can understand the nature of minds a priori - or at the very least grounds for individuals to argue as such. The success of explaining phenomena in the universe in terms of physics is something to take into account. After all, we are organised compositions of cells, which in turn are organised compositions of atoms. And modern brain sciences are confirming the notion that the mind is material, from brain injury to brain scans to magnetic stimulation of targeted areas - a physical mind is an inescapable conclusion.
Yet pretty much all arguments brought against the physicalist conclusion* all come from that internal view. The idea, it seems, is that for one to demonstrate the dualist nature of the mind one only has to think about it. While brain sciences are advancing, and technology is increasing the capabilities of what can be empirically observed, dualists are doing nothing to ground their arguments in empiricism.
It seems obvious enough what needs to be done, have a dualistic model that sits within the brain sciences where it can be put to the test. Descartes proposed the pineal gland as a potential solution to the mind-body interface problem nearly 400 years ago, these days the best we get are transmitter receiver analogies that don't pin themselves down to anything that's empirically useful.
The simplest way to put it is that we don't know the nature of what makes a mind through introspection. We can consider how a mind works, what kinds of phenomena need explanation, but none of that says anything about what makes a mind. This is where the necessity of empirical investigation comes in, because unless we want to appeal to magic we won't know what makes a mind by thinking about minds.
* At least the arguments I have come across